1. In Jane’s case #8, the students work on a problem about paint containers that is most literally represented by 4+3+1=8. Near the end of the case (line 54), Shiro presents 4+4=8 as his solution, and Charlene objects to this. How do you feel about Shiro’s solution? Does it model the problem? What is the point that Charlene is making? What connections do you see between the actions in the word problems and the student solutions?
2. In both Jody’s case 10 and Dolores’s case 11, the students display a variety of ways of solving a single problem. Examine each student’s method to determine what it shows you about his or her mental image of the action of the problem. What connections do you see between the actions in the word problems and the student solutions? How is it possible that the same problem can be solved by both and addition and a subtraction calculation? Where does this come up in other cases in this chapter?
3. Melinda (case 9) thought her students would solve an “Enough for the class” problem by first determining the whole amount and then subtracting to see what was left over. Did any children do this? Describe each child’s approach to the problem. Connect their methods with the actions they see in the situation.
4. Discuss the questions posed in the introductory text for this set of cases.
2. In both Jody’s case 10 and Dolores’s case 11, the students display a variety of ways of solving a single problem. Examine each student’s method to determine what it shows you about his or her mental image of the action of the problem. What connections do you see between the actions in the word problems and the student solutions? How is it possible that the same problem can be solved by both and addition and a subtraction calculation? Where does this come up in other cases in this chapter?
3. Melinda (case 9) thought her students would solve an “Enough for the class” problem by first determining the whole amount and then subtracting to see what was left over. Did any children do this? Describe each child’s approach to the problem. Connect their methods with the actions they see in the situation.
4. Discuss the questions posed in the introductory text for this set of cases.